The Probabilistic Collocation Method for Power-System Damping and Voltage Collapse Studies in the Presence of Uncertainties

This paper explores the feasibility of using the Probabilistic Collocation Method (PCM) in power-system studies in the presence of uncertainties. The application of the PCM is illustrated on small disturbance stability studies and voltage stability studies. First, the PCM is used to determine the effects of a supplementary power oscillation damping (POD) controller installed on a VSC-HVDC line in the presences of parameter and operational uncertainties. Second, it is used to calculate the probabilistic distance to voltage collapse in a distribution system based on measurement errors. The PCM is shown to produce accurate statistical results whilst drastically reducing the computational time of the studies in both cases. Additionally, a ranking process based on eigenvalue sensitivity is presented alongside the small disturbance analysis as an appropriate method for reduction of system complexity for extension to large power systems. This technique is validated through the application of the PCM on a large power-system model, yielding accurate probabilistic results.